What is a reliability block diagram?
A reliability block diagram shows the success paths through a system: the combinations of components that must work for the system to work. It is used in design to compare architectures, decide where redundancy is worth its cost and check whether a design can meet a reliability target, and in operations to understand which equipment the plant depends on most.
Series, parallel and k-out-of-n
| Configuration | System works when | Reliability |
|---|---|---|
| Series | All blocks work | R1 × R2 × … × Rn |
| Parallel | At least one block works | 1 − (1 − R1)(1 − R2)…(1 − Rn) |
| k-out-of-n | At least k of n blocks work | Σ binomial probabilities for k to n working |
Reliability block diagram example
A cooling water pump station must run for a 720-hour month. Power comes from the mains (MTBF 8,000 h) with a backup generator (3,000 h) in parallel, then a control PLC (50,000 h), then three pumps (4,000 h each) of which two are needed, then a discharge valve (R 0.995). The system reliability is 89.3%. Each pump has only an 83.5% chance of lasting the month, and improving the pumps gives the biggest gain: if one pump never failed, system reliability would rise by 4.4 points. The control PLC is the single point of failure (Birnbaum importance 0.91), but it is already 98.6% reliable, so the team starts with pump condition monitoring.
Tips
- Draw success paths, not the physical layout. Two valves physically in series may be in parallel in an RBD if either one can close the line.
- Use the same mission time for all blocks, and field MTBF where you have it: see the MTBF/MTTR analysis.
- Watch for common causes: redundant pumps fed by one power supply are not truly redundant.
- For wear-out components, use a Weibull analysis to get the reliability for the mission rather than a constant failure rate.
How to use this Reliability Block Diagram tool
- Set the mission. Name the system and enter the mission time over which it must work, for example 720 h.
- Build the diagram. Click a block and use + In series or + In parallel to add components; + at the bottom adds a block at the end of the main chain.
- Enter block data. For each block, enter its MTBF or its reliability for the mission.
- Set redundancy. Click a parallel group's label to set how many branches must work (k out of n).
- Read the result. The system reliability appears at the top; the table ranks the blocks by the gain from improving them.
- Export. Export the diagram and block table to PDF, PNG or Excel.
Frequently asked questions
What is a reliability block diagram?
A reliability block diagram (RBD) models how the reliability of a system depends on its components. Each component is a block; blocks in series must all work for the system to work, blocks in parallel provide redundancy. From the reliability of each block, the diagram gives the reliability of the whole system.
How is system reliability calculated?
For blocks in series, multiply their reliabilities: R = R1 × R2 × … For blocks in parallel (any one is enough), R = 1 − (1 − R1)(1 − R2)… For a k-out-of-n group, add the binomial probabilities that at least k of the n branches work. Groups can be nested, and the tool works from the inside out.
What is a k-out-of-n system?
A group of n identical or similar branches of which at least k must work, for example 2 of 3 pumps needed to meet demand. 1-out-of-n is full redundancy and n-out-of-n behaves like a series chain.
How do I get block reliability from MTBF?
With a constant failure rate (exponential model), R(t) = exp(−t / MTBF) for a mission time t. A block with an MTBF of 4,000 h has R = exp(−720 / 4000) = 0.835 over a 720 h month. Enter a reliability directly if you have test or field data for the mission.
Which block should I improve first?
The tool ranks blocks by improvement potential: how much system reliability would rise if the block never failed. It also reports Birnbaum importance, the drop in system reliability when the block fails, which identifies single points of failure.
What are the limits of an RBD?
A simple RBD assumes blocks fail independently, have two states (working or failed) and are not repaired during the mission. Common-cause failures (a shared power supply, a flood) and repairable systems need more advanced methods such as fault trees or Markov models.